Dishes
The HOD is to test at least three different dishes out of five before scoring the students. How many ways can he choose the dishes?
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Peter
Picking 3 out of 5 with the order not mattering is 5!/2!/3! where 3! is the number of ways to order the three dishes which we don't care about.
We do have to add picking 4 or even 5 dishes as the test states that at least three dishes have to be tested:
C3(5) + C4(5) + C5(5) = 10 + 5 + 1 = 16
We do have to add picking 4 or even 5 dishes as the test states that at least three dishes have to be tested:
C3(5) + C4(5) + C5(5) = 10 + 5 + 1 = 16
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